Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N=2e5+5;
int n,a[N],pos[N];
void init()
{
    int i;
    scanf("%d",&n);
    for(i=1;i<=n;++i) scanf("%d",&a[i]),pos[a[i]]=i;
}
void work()
{
    int i,cnt=0,now=0;
    for(i=n-1;i;--i)
    {
        if(!cnt)
        {
            if(pos[i]>pos[i+1]) ++cnt,now=i+1;
            continue;
        }
        if(pos[now]<=pos[i]&&pos[i]<=pos[i+1]) continue;
        if(pos[i]<=pos[i+1]&&pos[i+1]<=pos[now]) continue;
        if(pos[i+1]<=pos[now]&&pos[now]<=pos[i]) continue;
        ++cnt,now=i+1;
    }
    printf("%d\n",cnt);
}

int main()
{
    init();
    work();
    return 0;
}